Automatic speech understanding and speech synthesis, two of the major speech processing applications, impose strikingly different constraints and requirements on prosodic models. The prevalent models of prosody and intonation fail to offer a unified solution to these conflicting constraints. As a consequence, prosodic models have been applied only occasionally in end-to-end automatic speech understanding systems; in contrast, they have been applied extensively in speech synthesis systems. In this paper we want to discuss the reasons for this state of affairs as well as possible strategies to overcome the shortcomings of the use of prosodic modelling in automatic speech processing.